Skip to main content
SpringerLink
Log in

Note on the parity of broken 11-diamond partitions

  • Published:
The Ramanujan Journal Aims and scope Submit manuscript

Abstract

In this paper, we prove new infinite families of congruences modulo 2 for broken 11-diamond partitions by using Hecke operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ahmed, Z., Baruah, N.: Parity results for broken 5-diamond, 7-diamond and 11-diamond partitions. Int. J. Number Theory 11, 527–542 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  2. Andrews, G.E., Paule, P.: MacMahon’s partition analysis XI: broken diamonds and modular forms. Acta. Arith. 126, 281–294 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chan, H.H., Toh, P.C.: New analogues of Ramanujan spartition identities. J. Number Theory 129, 1898–1913 (2010)

    Article  MATH  Google Scholar 

  4. Chen, S.C.: On the number of partitions with distinct even parts. Discret. Math. 311(12), 940–943 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cox, D.A.: Primes of the Form \(x^2+ny^2\): Fermat, Class Field Theory, and Complex Multiplication. Wiley, New York (1989)

    Google Scholar 

  6. Koblitz, N.: Introduction to Elliptic Curves and Modular Forms. Graduate Texts in Mathematics, vol. 97. Springer, New York (1984)

    MATH  Google Scholar 

  7. Martin, Y.: Multiplicative \(\eta \)-quotients. Trans. Am. Math. Soc. 348, 4825–4856 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ono, K.: The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-Series. CBMS Regional Conferences Series in Mathematics, vol. 102. American Mathematical Society, Providence (2004)

    MATH  Google Scholar 

  9. Sun, Z.H., Williams, K.S.: On the number of representations of \(n\) by \(ax^2+bxy+cy^2\). Acta. Arith. 122, 101–171 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Yao, X.M.: New parity results for broken 11-diamond partitions. J. Number Theory 140, 267–276 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

We would like to thank the referee for his/her helpful comments.

Author information

Authors and Affiliations

  1. School of Science, Anhui University of Science and Technology Huainan, Anhui, 232001, China

    Haobo Dai

Authors
  1. Haobo Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haobo Dai.

Additional information

This research was supported by the National Natural Science Foundation of China (Grant No. 11501007).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dai, H. Note on the parity of broken 11-diamond partitions. Ramanujan J 42, 617–622 (2017). https://doi.org/10.1007/s11139-016-9794-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11139-016-9794-0

Keywords

Mathematics Subject Classification

Search

Navigation